Post-Lie Algebras, Factorization Theorems and Isospectral-Flows

In these notes we review and further explore the Lie enveloping algebra of a post-Lie algebra. From a Hopf algebra point of view, one of the central results, which will be recalled in detail, is the existence of a second Hopf algebra structure. By comparing group-like elements in suitable completions of these two Hopf algebras, we derive a particular map which we dub post-Lie Magnus expansion. These results are then considered in the case of Semenov-Tian-Shansky's double Lie algebra, where a post-Lie algebra is defined in terms of solutions of modified classical Yang-Baxter equation. In this context, we prove a factorization theorem for group-like elements. An explicit exponential solution of the corresponding Lie bracket flow is presented, which is based on the aforementioned post-Lie Magnus expansion.Comment: 49 pages, no-figures, review articl

Transboundary water interaction III: contest and compliance

This paper serves international water conflict resolution efforts by examining the ways that states contest hegemonic transboundary water arrangements. The conceptual framework of dynamic transboundary water interaction that it presents integrates theories about change and counter-hegemony to ascertain coercive, leverage, and liberating mechanisms through which contest and transformation of an arrangement occur. While the mechanisms can be active through sociopolitical processes either of compliance or of contest of the arrangement, most transboundary water interaction is found to contain elements of both. The role of power asymmetry is interpreted through classification of intervention strategies that seek to either influence or challenge the arrangements. Coexisting contest and compliance serve to explain in part the stasis on the Jordan and Ganges rivers (where the non-hegemons have in effect consented to the arrangement), as well as the changes on the Tigris and Mekong rivers, and even more rapid changes on the Amu Darya and Nile rivers (where the non-hegemons have confronted power asymmetry through influence and challenge). The framework also stresses how transboundary water events that may appear isolated are more accurately read within the many sociopolitical processes and arrangements they are shaped by. By clarifying the typically murky dynamics of interstate relations over transboundary waters, furthermore, the framework exposes a new suite of entry points for hydro-diplomatic initiatives

On the definition and examples of cones and finsler spacetimes

The authors warmly acknowledge Professor Daniel Azagra (Universidad Complutense, Madrid) his advise on approximation of convex functions as well as Profs. Kostelecky (Indiana University), Fuster (University of Technology, Eindhoven), Stavrinos (University of Athens), Pfeifer (University of Tartu), Perlick (University of Bremen) and Makhmali (Institute of Mathematics, Warsaw) their comments on a preliminary version of the article. The careful revision by the referee is also acknowledged. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Region de Murcia, Spain, by Fundacion Seneca, Science and Technology Agency of the Region de Murcia. MAJ was partially supported by MINECO/FEDER project reference MTM2015-65430-P and Fundacion Seneca project reference 19901/GERM/15, Spain and MS by Spanish MINECO/ERDF project reference MTM2016-78807-C2-1-P.A systematic study of (smooth, strong) cone structures C and Lorentz–Finsler metrics L is carried out. As a link between both notions, cone triples (Ω,T,F), where Ω (resp. T) is a 1-form (resp. vector field) with Ω(T)≡1 and F, a Finsler metric on ker(Ω), are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures C are bijectively associated with classes of anisotropically conformal metrics L, and the notion of cone geodesic is introduced consistently with both structures. As a non-relativistic application, the time-dependent Zermelo navigation problem is posed rigorously, and its general solution is provided.MINECO/FEDER project, Spain MTM2015-65430-PFundacion Seneca 19901/GERM/15Spanish MINECO/ERDF project MTM2016-78807-C2-1-

Use of Cis-[18F]Fluoro-Proline for Assessment of Exercise-Related Collagen Synthesis in Musculoskeletal Connective Tissue

Protein turnover in collagen rich tissue is influenced by exercise, but can only with difficulty be studied in vivo due to use of invasive procedure. The present study was done to investigate the possibility of applying the PET-tracer, cis-[18F]fluoro-proline (cis-Fpro), for non-invasive assessment of collagen synthesis in rat musculoskeletal tissues at rest and following short-term (3 days) treadmill running. Musculoskeletal collagen synthesis was studied in rats at rest and 24 h post-exercise. At each session, rats were PET scanned at two time points following injection of cis-FPro: (60 and 240 min p.i). SUV were calculated for Achilles tendon, calf muscle and tibial bone. The PET-derived results were compared to mRNA expression of collagen type I and III. Tibial bone had the highest SUV that increased significantly (p<0.001) from the early (60 min) to the late (240 min) PET scan, while SUV in tendon and muscle decreased (p<0.001). Exercise had no influence on SUV, which was contradicted by an increased gene expression of collagen type I and III in muscle and tendon. The clearly, visible uptake of cis-Fpro in the collagen-rich musculoskeletal tissues is promising for multi-tissue studies in vivo. The tissue-specific differences with the highest basal uptake in bone are in accordance with earlier studies relying on tissue incorporation of isotopic-labelled proline. A possible explanation of the failure to demonstrate enhanced collagen synthesis following exercise, despite augmented collagen type I and III transcription, is that SUV calculations are not sensitive enough to detect minor changes in collagen synthesis. Further studies including kinetic compartment modeling must be performed to establish whether cis-Fpro can be used for non-invasive in-vivo assessment of exercise-induced changes in musculoskeletal collagen synthesis

Tissue Type-Specific Expression of the dsRNA-Binding Protein 76 and Genome-Wide Elucidation of Its Target mRNAs

Background: RNA-binding proteins accompany all steps in the life of mRNAs and provide dynamic gene regulatory functions for rapid adjustment to changing extra-or intracellular conditions. The association of RNA-binding proteins with their targets is regulated through changing subcellular distribution, post-translational modification or association with other proteins. Methodology: We demonstrate that the dsRNA binding protein 76 (DRBP76), synonymous with nuclear factor 90, displays inherently distinct tissue type-specific subcellular distribution in the normal human central nervous system and in malignant brain tumors of glial origin. Altered subcellular localization and isoform distribution in malignant glioma indicate that tumor-specific changes in DRBP76-related gene products and their regulatory functions may contribute to the formation and/or maintenance of these tumors. To identify endogenous mRNA targets of DRBP76, we performed RNA-immunoprecipitation and genome-wide microarray analyses in HEK293 cells, and identified specific classes of transcripts encoding critical functions in cellular metabolism. Significance: Our data suggest that physiologic DRBP76 expression, isoform distribution and subcellular localization are profoundly altered upon malignant transformation. Thus, the functional role of DRBP76 in co- or post-transcriptional gene regulation may contribute to the neoplastic phenotype

E-Democracy and the European Public Sphere

The chapter starts with an outline of outstanding recent contributions to the discussion of the EU democratic deficit and the so-called “no demos” problem and the debate about European citizenship and European identity—mainly in the light of insights from the EU crisis. This is followed by reflections on the recent discussion on the state of the mass media-based European public sphere. Finally, the author discusses the state of research on the Internet’s capacity to support the emergence of a (renewed) public sphere, with a focus on options for political actors to use the Internet for communication and campaigning, on the related establishment of segmented issue-related publics as well as on social media and its two-faced character as an enabler as well as a distorting factor of the public sphere. The author is sceptic about the capacities of Internet-based political communication to develop into a supranational (European) public sphere. It rather establishes a network of a multitude of discursive processes aimed at opinion formation at various levels and on various issues. The potential of online communication to increase the responsiveness of political institutions so far is set into practice insufficiently. Online media are increasingly used in a vertical and scarcely in a horizontal or interactive manner of communication

MR imaging in sports-related glenohumeral instability

Sports-related shoulder pain and injuries represent a common problem. In this context, glenohumeral instability is currently believed to play a central role either as a recognized or as an unrecognized condition. Shoulder instabilities can roughly be divided into traumatic, atraumatic, and microtraumatic glenohumeral instabilities. In athletes, atraumatic and microtraumatic instabilities can lead to secondary impingement syndromes and chronic damage to intraarticular structures. Magnetic resonance (MR) arthrography is superior to conventional MR imaging in the diagnosis of labro-ligamentous injuries, intrinsic impingement, and SLAP (superior labral anteroposterior) lesions, and thus represents the most informative imaging modality in the overall assessment of glenohumeral instability. This article reviews the imaging criteria for the detection and classification of instability-related injuries in athletes with special emphasis on the influence of MR findings on therapeutic decisions